Geodesic
B-Stable Ideals in the Nilradical of a Borel Subalgebra
Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 460-472

Voir la notice de l'article provenant de la source Cambridge University Press

We count the number of strictly positive $B$ -stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any $B$ -stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.
DOI : 10.4153/CMB-2005-043-4
Mots-clés : 20F55, 17B20, 05E99 
Sommers, Eric N. B-Stable Ideals in the Nilradical of a Borel Subalgebra. Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 460-472. doi: 10.4153/CMB-2005-043-4
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[1] [1] Athanasiadis, C., Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes. Bull. London Math. Soc. 36(2004), 294–302. Google Scholar

[2] [2] Broer, A., Lectures on decomposition classes. In: Representation Theories and Algebraic Geometry, Nato Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514, Lkuwer, Dordrecht, 1998, pp. 39–83. Google Scholar

[3] [3] Cellini, P. and Papi, P., ad-nilpotent ideals of a Borel subalgebra. J. Algebra 225(2000), 130–141. Google Scholar

[4] [4] Cellini, P. and Papi, P., ad-nilpotent ideals of a Borel subalgebra. II. J. Algebra 258(2002), 112–121. Google Scholar

[5] [5] Douglass, J. M., The adjoint representation of a reductive group and hyperplane arrangements. Represen. Theory 3(1999), 444–456. Google Scholar

[6] [6] Fan, C. K., Euler characteristic of certain affine flag varieties. Transform. Groups 1(1996), 35–39. Google Scholar

[7] [7] Fomin, S. and Zelevinsky, A., Y -systems and generalized associahedra. Ann.of Math. 158(2003), 977–1018. Google Scholar

[8] [8] Haiman, M., Conjectures on the quotient ring by diagonal invariants. J. Algebraic Combin. 3(1994), 17–76. Google Scholar

[9] [9] Headley, P., On a family of hyperplane arrangements related to the affine Weyl groups. J. Algebraic Combin. 6(1997), 331–338. Google Scholar

[10] [10] Orlik, P. and Solomon, L., Coxeter arrangements. In: Singularities, Proc. Sympos Pure Math. 40, American Mathematical Society, Providence, RI, 1983, pp. 269–291. Google Scholar

[11] [11] Panyushev, D., Ad-nilpotent ideals of a Borel subalgebra: generators and duality, math.RT/0303107, 2003. Google Scholar

[12] [12] Shi, J.-Y., Sign types corresponding to an affine Weyl group. J. LondonMath. Soc.(2) 35(1987), 56–74. Google Scholar

[13] [13] Shi, J.-Y., The number of ⊕-sign types. Quart. J. Math. Oxford Ser. (2) 48(1997), 93–105. Google Scholar

[14] [14] Sommers, E., A family of affine Weyl group representations. Transform. Groups 2(1997), 375–390. Google Scholar

[15] [15] Sommers, E., A generalization of the Bala-Carter theorem for nilpotent orbits. Internat. Math. Res. Notices 1998, 539–562. Google Scholar

[16] [16] Terao, H., Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula. Invent.Math. 63(1981), 159–179. Google Scholar

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